Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-7y &= 2 \\ 8x+6y &= -2\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $6y = -8x-2$ Divide both sides by $6$ to isolate $y$ $y = {-\dfrac{4}{3}x - \dfrac{1}{3}}$ Substitute this expression for $y$ in the first equation. $-8x-7({-\dfrac{4}{3}x - \dfrac{1}{3}}) = 2$ $-8x + \dfrac{28}{3}x + \dfrac{7}{3} = 2$ Simplify by combining terms, then solve for $x$ $\dfrac{4}{3}x + \dfrac{7}{3} = 2$ $\dfrac{4}{3}x = -\dfrac{1}{3}$ $x = -\dfrac{1}{4}$ Substitute $-\dfrac{1}{4}$ for $x$ back into the top equation. $-8( -\dfrac{1}{4})-7y = 2$ $2-7y = 2$ $-7y = 0$ $y = 0$ The solution is $\enspace x = -\dfrac{1}{4}, \enspace y = 0$.